Perturbative corrections to general relativity alter the expressions for both the entropy of black holes and their extremality bounds. We prove a universal relation between the leading corrections to these quantities. The derivation is purely thermodynamic and the result also applies beyond the realm of gravitational systems. In scenarios where the correction to the entropy is positive, our result proves that the perturbations decrease the mass of extremal black holes, when holding all other extensive variables fixed in the comparison. This implies that the extremality relations of a wide class of black holes display weak gravity conjecture-like behavior.

• Received 30 September 2019
• Revised 20 December 2019
• Accepted 27 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.101103

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Published by the American Physical Society